A Set Of Examples Of Global And Discrete Optimization

This book shows how to improve well-known heuristics by randomizing and optimizing their parameters. The ten in-depth examples are designed to teach operations research and the theory of games and markets using the Internet. Each example is a simple representation of some important family of real-life problems. Remote Internet users can run the accompanying software. The supporting web sites include software for Java, C++, and other languages. Audience: Researchers and specialists in operations research, systems engineering and optimization methods, as well as Internet applications experts in the fields of economics, industrial and applied mathematics, computer science, engineering, and environmental sciences.

This book shows how the Bayesian Approach (BA) improves well known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some impor tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lan guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization prob lems. The techniques are evaluated in the spirit of the average rather than the worst case analysis. In this context, "heuristics" are understood to be an expert opinion defining how to solve a family of problems of dis crete or global optimization. The term "Bayesian Heuristic Approach" means that one defines a set of heuristics and fixes some prior distribu tion on the results obtained. By applying BHA one is looking for the heuristic that reduces the average deviation from the global optimum. The theoretical discussions serve as an introduction to examples that are the main part of the book. All the examples are interconnected. Dif ferent examples illustrate different points of the general subject. How ever, one can consider each example separately, too.

Global optimization is a branch of applied mathematics and numerical analysis that deals with the task of finding the absolutely best set of admissible conditions to satisfy certain criteria / objective function(s), formulated in mathematical terms. Global optimization includes nonlinear, stochastic and combinatorial programming, multiobjective programming, control, games, geometry, approximation, algorithms for parallel architectures and so on. Due to its wide usage and applications, it has gained the attention of researchers and practitioners from a plethora of scientific domains. Typical practical examples of global optimization applications include: Traveling salesman problem and electrical circuit design (minimize the path length); safety engineering (building and mechanical structures); mathematical problems (Kepler conjecture); Protein structure prediction (minimize the energy function) etc. Global Optimization algorithms may be categorized into several types: Deterministic (example: branch and bound methods), Stochastic optimization (example: simulated annealing). Heuristics and meta-heuristics (example: evolutionary algorithms) etc. Recently there has been a growing interest in combining global and local search strategies to solve more complicated optimization problems. This edited volume comprises 17 chapters, including several overview Chapters, which provides an up-to-date and state-of-the art research covering the theory and algorithms of global optimization. Besides research articles and expository papers on theory and algorithms of global optimization, papers on numerical experiments and on real world applications were also encouraged. The book is divided into 2 main parts.

The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.

The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ``Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.